Q1:

Determine the equation of the tangent line to the path r(t) = (sin(4f), cos(4t), 1215/12) at t = 1. (Write your solution using the form (*,*,*). Use symbolic notation and fractions where needed. Use the equation of the tangent line such that the point of tangency occurs when t = 1.) tangent line: l(t) = I Suppose that a particle following the path C(t) = (t2, t3 5t, 0) ies off on a tangent at to = 3. Compute the position of the particle at the time 11 = 5. (Enter your answer in the vector form (*,*,*). Use symbolic notation and fractions where needed.) position at time t1 = l Find the arc length of the curve c(t) = (S cos(t), 5 sin(t), l3t) on the interval 0 5 t 5 21:. (Express numbers in exact form. Use symbolic notation and fractions where needed.) L(c) = Calculate the velocity and acceleration vectors for the helix c(t) = (8 cos(t), 8 sin(t), 3t) at r = g (Express numbers in exact form. Use symbolic notation and fractions Where needed. Give your answer in the form (*,*,*))